1. **Problem statement:** Given a right triangle XYZ with right angle at Y, altitude YW to hypotenuse XZ, and segments XW = r, WZ = s, find the altitude $h$. 2. **Formula used:** In a right triangle with altitude to hypotenuse, the altitude $h$ satisfies: $$h = \sqrt{r \times s}$$ where $r$ and $s$ are the segments into which the altitude divides the hypotenuse. 3. **Given:** $r = 12$, $s = 3$ 4. **Calculate:** $$h = \sqrt{12 \times 3} = \sqrt{36} = 6$$ 5. **Answer:** $$h = 6$$ This uses the property that the altitude to the hypotenuse in a right triangle is the geometric mean of the two segments it creates on the hypotenuse.